{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:40:58Z","timestamp":1753886458833,"version":"3.41.2"},"reference-count":16,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2010,7,29]],"date-time":"2010-07-29T00:00:00Z","timestamp":1280361600000},"content-version":"vor","delay-in-days":209,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>For each <jats:italic>N<\/jats:italic> \u2265 4, we define a monoidal functor from Elias and Khovanov\u2032s diagrammatic\nversion of Soergel\u2032s category of bimodules to the category of <jats:italic>s<\/jats:italic><jats:italic>l<\/jats:italic>(<jats:italic>N<\/jats:italic>) foams defined by Mackaay, Sto\u0161i\u0107, and Vaz. We show that through these functors Soergel\u2032s category can be obtained\nfrom the <jats:italic>s<\/jats:italic><jats:italic>l<\/jats:italic>(<jats:italic>N<\/jats:italic>) foams.<\/jats:p>","DOI":"10.1155\/2010\/468968","type":"journal-article","created":{"date-parts":[[2010,7,29]],"date-time":"2010-07-29T21:37:48Z","timestamp":1280439468000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The Diagrammatic Soergel Category and <i>s<\/i><i>l<\/i>(<i>N<\/i>)\u2010Foams, for <i>N<\/i> \u2265 4"],"prefix":"10.1155","volume":"2010","author":[{"given":"Marco","family":"Mackaay","sequence":"first","affiliation":[]},{"given":"Pedro","family":"Vaz","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,7,29]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1992.429.49"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2008.12.1387"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0129167X07004400"},{"key":"e_1_2_6_4_2","doi-asserted-by":"crossref","unstructured":"EliasB.andKhovanovM. Diagrammatics for Soergel categories http:\/\/arxiv.org\/abs\/0902.4700v1 https:\/\/doi.org\/10.2140\/gt.2005.9.1443.","DOI":"10.2140\/gt.2005.9.1443"},{"key":"e_1_2_6_5_2","doi-asserted-by":"crossref","unstructured":"EliasB.andKrasnerD. Rouquier complexes are functorial over braid cobordisms http:\/\/arxiv.org\/abs\/0906.4761 https:\/\/doi.org\/10.2140\/gt.2005.9.1443.","DOI":"10.2140\/gt.2005.9.1443"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2005.9.1443"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012\u20107094\u201000\u201010\u20107"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2004.4.1045"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm199\u20101\u20101"},{"key":"e_1_2_6_10_2","doi-asserted-by":"crossref","unstructured":"RasmussenJ. Some differentials on Khovanov-Rozansky homology http:\/\/arxiv.org\/abs\/math.GT\/0607544 https:\/\/doi.org\/10.2140\/gt.2009.13.1075.","DOI":"10.2140\/gt.2009.13.1075"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2009.13.1075"},{"key":"e_1_2_6_12_2","doi-asserted-by":"crossref","first-page":"727","DOI":"10.4310\/ATMP.2003.v7.n4.a5","article-title":"Topological correlators in Landau-Ginzburg models with boundaries","volume":"7","author":"Kapustin A.","year":"2003","journal-title":"Advances in Theoretical and Mathematical Physics"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.4310\/ATMP.2007.v11.n2.a2"},{"key":"e_1_2_6_14_2","unstructured":"VazP. The diagrammatic Soergel category andsl(2) andsl(3) foams International Journal of Mathematics and Mathematical Sciences http:\/\/arxiv.org\/abs\/0909.3495."},{"key":"e_1_2_6_15_2","doi-asserted-by":"crossref","first-page":"1679","DOI":"10.1353\/ajm.0.0082","article-title":"A combinatorial approach to functorial quantum s\n                  l(k)  knot\ninvariants","volume":"131","author":"Mazorchuk V.","year":"2009","journal-title":"American Journal of Mathematics"},{"key":"e_1_2_6_16_2","unstructured":"VazP. A categorification of the quantum sl(N)-link polynomials using foams Ph.D. thesis 2008 Universidade do Algarve."}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2010\/468968.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2010\/468968.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2010\/468968","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T16:28:11Z","timestamp":1718728091000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2010\/468968"}},"subtitle":[],"editor":[{"given":"Aaron","family":"Lauda","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1155\/2010\/468968"],"URL":"https:\/\/doi.org\/10.1155\/2010\/468968","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2010,1]]},"assertion":[{"value":"2009-11-17","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-04-10","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-07-29","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"468968"}}